I don't know where to begin with this question. Could someone help me please?

A rod of mass 4.1 kg and length 1.6 m hangs from a hinge as shown in the figure below. The end of the rod is then given a "kick" so that it is moving at a speed of 5 m/s. How high will the rod swing? Express your answer in terms of the angle the rod makes with the vertical.

The angular momentum of the rod right after the kick is given by
I*w = (1/3)M*L^2*w
where w = ( 5 m/s)/L = 3.13 rad/s
I*w = 10.95 kg*m^2/s

Next, compute the total kinetic energy at the start of the upward swing.

KE(max) = (1/2)*(I*w)*w

That equals the increase in potential energy at maximum deflection angle A. That angle is determined by the center of mass location.

Check my thinking. I am leaving the rest up to you.

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